That only is a problem if you don't separate the 'time number' from the observed local time.

You could easily have a 'multiple calendar days during one solarday' situation. In fact, many countries already do this for their TV programming, in which a show might screen on "Thursday at 23:55 until 03:15".

For common things, you could just refer to as 'tomorrow morning'. If you need more precision, you can fall back to .beats. "School starts @740" Incidentally, that's exactly why I liked .beats: no false associations.